A pump control device for a construction machine includes a pump regulator, a pump pressure detector, a travelling operation detector, a working operation detector, and a controller instructing the pump flow rate depending on the pump pressure to the pump regulator. The controller stores first and second P-Q characteristics as a horsepower characteristic and instructs the pump flow rate to the pump regulator, based on the first P-Q characteristic when a travelling operation is detected, and based on the second P-Q characteristic when a working operation is detected. The second P-Q characteristic is equal to the first P-Q characteristic in a low-pressure region while is one giving a low characteristic relatively to the first P-Q characteristic so as to increase a horsepower difference as the pump pressure increases, in intermediate-pressure and high-pressure regions.